Question

How do you solve $\dfrac{2x}{x-4}=\dfrac{8}{x-4}+3$?

Answer 1

Hint: To solve the given equation we have to simplify the given equation furthermore. Certain transformations and substitutions should be made to get the equation simplified and to get the value of $x$. And finally verification should be done to check whether the value of $x$ we get is correct or not.

Complete step by step answer:
From the question it had been given that, $\dfrac{2x}{x-4}=\dfrac{8}{x-4}+3$
To get the process easier and to get the above equation more simplified
We have to multiply the both sides of the equation with $x-4$
By multiplying the equation with $x-4$ on both sides we get the below equation,
$2x=8+3\left( x-4 \right)$
On furthermore simplification of the above step we get,
$2x=8+3x-12$
On solving the equation we get,
$x=4$
By using the certain substitutions and transformations we get the value of $x=4$
Now verification should be done as we have been already discussed earlier to check whether we got the exact value or not.
Verification:
First we have to verify the left hand side of the equation,
Left hand side:
$\dfrac{2x}{x-4}=\dfrac{8}{4-4}$
$\dfrac{2x}{x-4}=\dfrac{8}{0}$
Here we got the result as undefined.
Now, we have to verify the right hand side of the equation,
Right hand side:
$\dfrac{8}{x-4}+3=\dfrac{8}{4-4}+3$
$\dfrac{8}{x-4}+3=\dfrac{8}{0}+3$
Here also we got the result as undefined.
Therefore we got the value $x=4$ when we did the calculation, but when we did the verification process it is not verified.
Hence for the given equation there is no solution.

Note: We should be careful while doing calculations while doing this type of problems. In this type of problem students should do the verification process in the last to check whether the value we got is correct or not. We should simplify the given equation into a simpler way so that problem can be solved easily. For simplifying this expression $\dfrac{2x}{x-4}=\dfrac{8}{x-4}+3$ we can directly write the answer as $x=4$ but we have to note that for fractions the denominator should not be zero so $x=4$ is not the correct answer.